Ejemplo n.º 1
0
void Transformer::transform(int timeMoment) {
    /* precomputation (for NFFT, node-dependent) */
	if (timeMoment <= 0) { // first time
		nfsft_precompute_x(&plan);
	}

    /* Direct adjoint transformation, display result. */
    nfsft_adjoint_direct(&plan);

    string timeMomentStr;
    if (timeMoment >= 0) {
    	timeMomentStr = to_string(timeMoment) + " ";
    }

    //ofstream decomp_out(string("decomp") + suffixStr + ".txt");
    for (int k = 0; k <= plan.N; k++) {
    	double power = 0;
        for (int n = -k; n <= k; n++) {
        	if (decompOrPower) {
        		result_out << timeMomentStr << k << " " << n << " " << plan.f_hat[NFSFT_INDEX(k, n, &plan)][0] << " " << plan.f_hat[NFSFT_INDEX(k, n, &plan)][1] << endl;
        	} else {
        		auto re = plan.f_hat[NFSFT_INDEX(k, n, &plan)][0];
        		auto im = plan.f_hat[NFSFT_INDEX(k, n, &plan)][1];
        		power += re * re + im * im;
        	}
        }
        power /= (2 * k + 1);
    	if (!decompOrPower) {
    		result_out << timeMomentStr << k << " " << power << endl;
    	}
    }
    result_out.flush();

	//#ifdef ONLY_AZIMUTHAL_RECONST
    //	// Set all nonazimuthal waves to zero
	//	for (int k = 0; k <= plan.N; k++) {
	//		for (int n = -k+1; n <= k-1; n++) {
	//			plan.f_hat[NFSFT_INDEX(k,n,&plan)][0] = 0;
	//			plan.f_hat[NFSFT_INDEX(k,n,&plan)][1] = 0;
	//		}
	//	}
	//#endif

    if (reconst_out) {
		/* Direct transformation, display result. */
		nfsft_trafo_direct(&plan);

		//ofstream reconst_out(string("reconst") + suffixStr + ".txt");
		for (int m = 0; m < plan.M_total; m++) {
			*reconst_out << timeMomentStr << plan.x[2*m] << " " << plan.x[2*m + 1] << " " << plan.f[m][0] << " " << plan.f[m][1] << endl;
		}
		reconst_out->flush();
    }

    if (timeMoment < 0) { // only single transform
    	finalize();
    }
}
Ejemplo n.º 2
0
int
mfield_sht_calc(const gsl_vector *g, const double r,
                const gsl_vector *theta,
                const gsl_vector *phi, gsl_vector *Y,
                gsl_vector *Z,
                mfield_sht_workspace *w)
{
  const size_t M = w->M;

  if (theta->size != M)
    {
      GSL_ERROR("theta vector has wrong length", GSL_EBADLEN);
    }
  else if (phi->size != M)
    {
      GSL_ERROR("phi vector has wrong length", GSL_EBADLEN);
    }
  else if (Y->size != M)
    {
      GSL_ERROR("Y vector has wrong length", GSL_EBADLEN);
    }
  else if (Z->size != M)
    {
      GSL_ERROR("Z vector has wrong length", GSL_EBADLEN);
    }
  else
    {
      int s = GSL_SUCCESS;
      size_t i;

      /* scale phi to [-1/2,1/2] and theta to [0,1/2] for input to nfsft */
      for (i = 0; i < M; ++i)
        {
          double ti = gsl_vector_get(theta, i) / (2.0 * M_PI);
          double pi = gsl_vector_get(phi, i) / (2.0 * M_PI);

          if (pi >= 0.5)
            pi -= 1.0;

          w->plan.x[2*i] = pi;
          w->plan.x[2*i + 1] = ti;
        }

      /* node-dependent precomputation */
      nfsft_precompute_x(&(w->plan));

      /* perform vector transforms */
      transform_Y(g, r, theta, Y, w);
      transform_Z(g, r, Z, w);

      return s;
    }
}
Ejemplo n.º 3
0
/**
 * The main program.
 *
 * \param argc The number of arguments
 * \param argv An array containing the arguments as C-strings
 *
 * \return Exit code
 *
 * \author Jens Keiner
 */
int main (int argc, char **argv)
{
  int T;
  int N;
  int M;
  int M2;

  int t;                       /* Index variable for testcases                */
  nfsft_plan plan;             /* NFSFT plan                                  */
  nfsft_plan plan2;            /* NFSFT plan                                  */
  solver_plan_complex iplan;           /* NFSFT plan                                  */
  int j;                       /*                                             */
  int k;                       /*                                             */
  int m;                       /*                                             */
  int use_nfsft;               /*                                             */
  int use_nfft;                /*                                             */
  int use_fpt;                 /*                                             */
  int cutoff;                  /**< The current NFFT cut-off parameter        */
  double threshold;            /**< The current NFSFT threshold parameter     */
  double re;
  double im;
  double a;
  double *scratch;
  double xs;
  double *ys;
  double *temp;
  double _Complex *temp2;
  int qlength;
  double *qweights;
  fftw_plan fplan;
  fpt_set set;
  int npt;
  int npt_exp;
  double *alpha, *beta, *gamma;

  /* Read the number of testcases. */
  fscanf(stdin,"testcases=%d\n",&T);
  fprintf(stderr,"%d\n",T);

  /* Process each testcase. */
  for (t = 0; t < T; t++)
  {
    /* Check if the fast transform shall be used. */
    fscanf(stdin,"nfsft=%d\n",&use_nfsft);
    fprintf(stderr,"%d\n",use_nfsft);
    if (use_nfsft != NO)
    {
      /* Check if the NFFT shall be used. */
      fscanf(stdin,"nfft=%d\n",&use_nfft);
      fprintf(stderr,"%d\n",use_nfsft);
      if (use_nfft != NO)
      {
        /* Read the cut-off parameter. */
        fscanf(stdin,"cutoff=%d\n",&cutoff);
        fprintf(stderr,"%d\n",cutoff);
      }
      else
      {
        /* TODO remove this */
        /* Initialize unused variable with dummy value. */
        cutoff = 1;
      }
      /* Check if the fast polynomial transform shall be used. */
      fscanf(stdin,"fpt=%d\n",&use_fpt);
      fprintf(stderr,"%d\n",use_fpt);
      if (use_fpt != NO)
      {
        /* Read the NFSFT threshold parameter. */
        fscanf(stdin,"threshold=%lf\n",&threshold);
        fprintf(stderr,"%lf\n",threshold);
      }
      else
      {
        /* TODO remove this */
        /* Initialize unused variable with dummy value. */
        threshold = 1000.0;
      }
    }
    else
    {
      /* TODO remove this */
      /* Set dummy values. */
      use_nfft = NO;
      use_fpt = NO;
      cutoff = 3;
      threshold = 1000.0;
    }

    /* Read the bandwidth. */
    fscanf(stdin,"bandwidth=%d\n",&N);
    fprintf(stderr,"%d\n",N);

    /* Do precomputation. */
    nfsft_precompute(N,threshold,
      ((use_nfsft==NO)?(NFSFT_NO_FAST_ALGORITHM):(0U/*NFSFT_NO_DIRECT_ALGORITHM*/)), 0U);

    /* Read the number of nodes. */
    fscanf(stdin,"nodes=%d\n",&M);
    fprintf(stderr,"%d\n",M);

    /* */
    if ((N+1)*(N+1) > M)
    {
      X(next_power_of_2_exp)(N, &npt, &npt_exp);
      fprintf(stderr, "npt = %d, npt_exp = %d\n", npt, npt_exp);
      fprintf(stderr,"Optimal interpolation!\n");
      scratch = (double*) nfft_malloc(4*sizeof(double));
      ys = (double*) nfft_malloc((N+1)*sizeof(double));
      temp = (double*) nfft_malloc((2*N+1)*sizeof(double));
      temp2 = (double _Complex*) nfft_malloc((N+1)*sizeof(double _Complex));

      a = 0.0;
      for (j = 0; j <= N; j++)
      {
        xs = 2.0 + (2.0*j)/(N+1);
        ys[j] = (2.0-((j == 0)?(1.0):(0.0)))*4.0*nfft_bspline(4,xs,scratch);
        //fprintf(stdout,"%3d: g(%le) = %le\n",j,xs,ys[j]);
        a += ys[j];
      }
      //fprintf(stdout,"a = %le\n",a);
      for (j = 0; j <= N; j++)
      {
        ys[j] *= 1.0/a;
      }

      qlength = 2*N+1;
      qweights = (double*) nfft_malloc(qlength*sizeof(double));

      fplan = fftw_plan_r2r_1d(N+1, qweights, qweights, FFTW_REDFT00, 0U);
      for (j = 0; j < N+1; j++)
      {
        qweights[j] = -2.0/(4*j*j-1);
      }
      fftw_execute(fplan);
      qweights[0] *= 0.5;

      for (j = 0; j < N+1; j++)
      {
        qweights[j] *= 1.0/(2.0*N+1.0);
        qweights[2*N+1-1-j] = qweights[j];
      }

      fplan = fftw_plan_r2r_1d(2*N+1, temp, temp, FFTW_REDFT00, 0U);
      for (j = 0; j <= N; j++)
      {
        temp[j] = ((j==0 || j == 2*N)?(1.0):(0.5))*ys[j];
      }
      for (j = N+1; j < 2*N+1; j++)
      {
        temp[j] = 0.0;
      }
      fftw_execute(fplan);

      for (j = 0; j < 2*N+1; j++)
      {
        temp[j] *= qweights[j];
      }

      fftw_execute(fplan);

      for (j = 0; j < 2*N+1; j++)
      {
        temp[j] *= ((j==0 || j == 2*N)?(1.0):(0.5));
        if (j <= N)
        {
          temp2[j] = temp[j];
        }
      }

      set = fpt_init(1, npt_exp, 0U);

      alpha = (double*) nfft_malloc((N+2)*sizeof(double));
      beta = (double*) nfft_malloc((N+2)*sizeof(double));
      gamma = (double*) nfft_malloc((N+2)*sizeof(double));

      alpha_al_row(alpha, N, 0);
      beta_al_row(beta, N, 0);
      gamma_al_row(gamma, N, 0);

      fpt_precompute(set, 0, alpha, beta, gamma, 0, 1000.0);

      fpt_transposed(set,0, temp2, temp2, N, 0U);

      fpt_finalize(set);

      nfft_free(alpha);
      nfft_free(beta);
      nfft_free(gamma);

      fftw_destroy_plan(fplan);

      nfft_free(scratch);
      nfft_free(qweights);
      nfft_free(ys);
      nfft_free(temp);
    }

    /* Init transform plans. */
    nfsft_init_guru(&plan, N, M,
      ((use_nfft!=0)?(0U):(NFSFT_USE_NDFT)) |
      ((use_fpt!=0)?(0U):(NFSFT_USE_DPT)) | NFSFT_MALLOC_F | NFSFT_MALLOC_X |
      NFSFT_MALLOC_F_HAT | NFSFT_NORMALIZED | NFSFT_ZERO_F_HAT,
      PRE_PHI_HUT | PRE_PSI | FFTW_INIT |
      FFT_OUT_OF_PLACE,
      cutoff);

    if ((N+1)*(N+1) > M)
    {
      solver_init_advanced_complex(&iplan, (nfft_mv_plan_complex*)(&plan), CGNE | PRECOMPUTE_DAMP);
    }
    else
    {
      solver_init_advanced_complex(&iplan, (nfft_mv_plan_complex*)(&plan), CGNR | PRECOMPUTE_WEIGHT | PRECOMPUTE_DAMP);
    }

    /* Read the nodes and function values. */
    for (j = 0; j < M; j++)
    {
      fscanf(stdin,"%le %le %le %le\n",&plan.x[2*j+1],&plan.x[2*j],&re,&im);
      plan.x[2*j+1] = plan.x[2*j+1]/(2.0*PI);
      plan.x[2*j] = plan.x[2*j]/(2.0*PI);
      if (plan.x[2*j] >= 0.5)
      {
        plan.x[2*j] = plan.x[2*j] - 1;
      }
      iplan.y[j] = re + _Complex_I * im;
      fprintf(stderr,"%le %le %le %le\n",plan.x[2*j+1],plan.x[2*j],
        creal(iplan.y[j]),cimag(iplan.y[j]));
    }

    /* Read the number of nodes. */
    fscanf(stdin,"nodes_eval=%d\n",&M2);
    fprintf(stderr,"%d\n",M2);

    /* Init transform plans. */
    nfsft_init_guru(&plan2, N, M2,
      ((use_nfft!=0)?(0U):(NFSFT_USE_NDFT)) |
      ((use_fpt!=0)?(0U):(NFSFT_USE_DPT)) | NFSFT_MALLOC_F | NFSFT_MALLOC_X |
      NFSFT_MALLOC_F_HAT | NFSFT_NORMALIZED | NFSFT_ZERO_F_HAT,
      PRE_PHI_HUT | PRE_PSI | FFTW_INIT |
      FFT_OUT_OF_PLACE,
      cutoff);

    /* Read the nodes and function values. */
    for (j = 0; j < M2; j++)
    {
      fscanf(stdin,"%le %le\n",&plan2.x[2*j+1],&plan2.x[2*j]);
      plan2.x[2*j+1] = plan2.x[2*j+1]/(2.0*PI);
      plan2.x[2*j] = plan2.x[2*j]/(2.0*PI);
      if (plan2.x[2*j] >= 0.5)
      {
        plan2.x[2*j] = plan2.x[2*j] - 1;
      }
      fprintf(stderr,"%le %le\n",plan2.x[2*j+1],plan2.x[2*j]);
    }

    nfsft_precompute_x(&plan);

    nfsft_precompute_x(&plan2);

    /* Frequency weights. */
    if ((N+1)*(N+1) > M)
    {
      /* Compute Voronoi weights. */
      //nfft_voronoi_weights_S2(iplan.w, plan.x, M);

      /* Print out Voronoi weights. */
      /*a = 0.0;
      for (j = 0; j < plan.M_total; j++)
      {
        fprintf(stderr,"%le\n",iplan.w[j]);
        a += iplan.w[j];
      }
      fprintf(stderr,"sum = %le\n",a);*/

      for (j = 0; j < plan.N_total; j++)
      {
        iplan.w_hat[j] = 0.0;
      }

      for (k = 0; k <= N; k++)
      {
        for (j = -k; j <= k; j++)
        {
          iplan.w_hat[NFSFT_INDEX(k,j,&plan)] = 1.0/(pow(k+1.0,2.0)); /*temp2[j]*/;
        }
      }
    }
    else
    {
      for (j = 0; j < plan.N_total; j++)
      {
        iplan.w_hat[j] = 0.0;
      }

      for (k = 0; k <= N; k++)
      {
        for (j = -k; j <= k; j++)
        {
          iplan.w_hat[NFSFT_INDEX(k,j,&plan)] = 1/(pow(k+1.0,2.5));
        }
      }

      /* Compute Voronoi weights. */
      nfft_voronoi_weights_S2(iplan.w, plan.x, M);

      /* Print out Voronoi weights. */
      a = 0.0;
      for (j = 0; j < plan.M_total; j++)
      {
        fprintf(stderr,"%le\n",iplan.w[j]);
        a += iplan.w[j];
      }
      fprintf(stderr,"sum = %le\n",a);
    }

    fprintf(stderr, "N_total = %d\n", plan.N_total);
    fprintf(stderr, "M_total = %d\n", plan.M_total);

    /* init some guess */
    for (k = 0; k < plan.N_total; k++)
    {
      iplan.f_hat_iter[k] = 0.0;
    }

    /* inverse trafo */
    solver_before_loop_complex(&iplan);

    /*for (k = 0; k < plan.M_total; k++)
    {
      printf("%le %le\n",creal(iplan.r_iter[k]),cimag(iplan.r_iter[k]));
    }*/

    for (m = 0; m < 29; m++)
    {
      fprintf(stderr,"Residual ||r||=%e,\n",sqrt(iplan.dot_r_iter));
      solver_loop_one_step_complex(&iplan);
    }

    /*NFFT_SWAP_complex(iplan.f_hat_iter, plan.f_hat);
    nfsft_trafo(&plan);
    NFFT_SWAP_complex(iplan.f_hat_iter, plan.f_hat);

    a = 0.0;
    b = 0.0;
    for (k = 0; k < plan.M_total; k++)
    {
      printf("%le %le %le\n",cabs(iplan.y[k]),cabs(plan.f[k]),
        cabs(iplan.y[k]-plan.f[k]));
      a += cabs(iplan.y[k]-plan.f[k])*cabs(iplan.y[k]-plan.f[k]);
      b += cabs(iplan.y[k])*cabs(iplan.y[k]);
    }

    fprintf(stderr,"relative error in 2-norm: %le\n",a/b);*/

    NFFT_SWAP_complex(iplan.f_hat_iter, plan2.f_hat);
    nfsft_trafo(&plan2);
    NFFT_SWAP_complex(iplan.f_hat_iter, plan2.f_hat);
    for (k = 0; k < plan2.M_total; k++)
    {
      fprintf(stdout,"%le\n",cabs(plan2.f[k]));
    }

    solver_finalize_complex(&iplan);

    nfsft_finalize(&plan);

    nfsft_finalize(&plan2);

    /* Delete precomputed data. */
    nfsft_forget();

    if ((N+1)*(N+1) > M)
    {
      nfft_free(temp2);
    }

  } /* Process each testcase. */

  /* Return exit code for successful run. */
  return EXIT_SUCCESS;
}
Ejemplo n.º 4
0
void bench_openmp(int trafo_adjoint, int N, int M, double *x, C *f_hat, C *f, int m, int nfsft_flags, int psi_flags)
{
  nfsft_plan plan;
  int k, n;
//  int N, M, trafo_adjoint;
  int t, j;
  ticks t0, t1;
  double tt_total, tt_pre;

//  fscanf(infile, "%d %d %d", &trafo_adjoint, &N, &M);

/*#ifdef _OPENMP
  fftw_import_wisdom_from_filename("nfsft_benchomp_detail_threads.plan");
#else
  fftw_import_wisdom_from_filename("nfsft_benchomp_detail_single.plan");
#endif*/

  /* precomputation (for fast polynomial transform) */
//  nfsft_precompute(N,1000.0,0U,0U);

  /* Initialize transform plan using the guru interface. All input and output
   * arrays are allocated by nfsft_init_guru(). Computations are performed with
   * respect to L^2-normalized spherical harmonics Y_k^n. The array of spherical
   * Fourier coefficients is preserved during transformations. The NFFT uses a
   * cut-off parameter m = 6. See the NFFT 3 manual for details.
   */
  nfsft_init_guru(&plan, N, M, nfsft_flags | NFSFT_MALLOC_X | NFSFT_MALLOC_F |
    NFSFT_MALLOC_F_HAT | NFSFT_NORMALIZED | NFSFT_PRESERVE_F_HAT,
    PRE_PHI_HUT | psi_flags | FFTW_INIT | FFT_OUT_OF_PLACE, m);

/*#ifdef _OPENMP
  fftw_export_wisdom_to_filename("nfsft_benchomp_detail_threads.plan");
#else
  fftw_export_wisdom_to_filename("nfsft_benchomp_detail_single.plan");
#endif*/

  for (j=0; j < plan.M_total; j++)
  {
    for (t=0; t < 2; t++)
 //     fscanf(infile, "%lg", plan.x+2*j+t);
      plan.x[2*j+t] = x[2*j+t];
  }

  if (trafo_adjoint==0)
  {
    memset(plan.f_hat,0U,plan.N_total*sizeof(double _Complex));
    for (k = 0; k <= plan.N; k++)
      for (n = -k; n <= k; n++)
      {
//        fscanf(infile, "%lg %lg", &re, &im);
//        plan.f_hat[NFSFT_INDEX(k,n,&plan)] = re + _Complex_I * im;
        plan.f_hat[NFSFT_INDEX(k,n,&plan)] = f_hat[NFSFT_INDEX(k,n,&plan)];
      }
  }
  else
  {
    for (j=0; j < plan.M_total; j++)
    {
//      fscanf(infile, "%lg %lg", &re, &im);
//      plan.f[j] = re + _Complex_I * im;
      plan.f[j] = f[j];
    }

    memset(plan.f_hat,0U,plan.N_total*sizeof(double _Complex));
  }

  t0 = getticks();
  /* precomputation (for NFFT, node-dependent) */
  nfsft_precompute_x(&plan);
  t1 = getticks();
  tt_pre = nfft_elapsed_seconds(t1,t0);

  if (trafo_adjoint==0)
    nfsft_trafo(&plan);
  else
    nfsft_adjoint(&plan);
  t1 = getticks();
  tt_total = nfft_elapsed_seconds(t1,t0);

#ifndef MEASURE_TIME
  plan.MEASURE_TIME_t[0] = 0.0;
  plan.MEASURE_TIME_t[2] = 0.0;
#endif

#ifndef MEASURE_TIME_FFTW
  plan.MEASURE_TIME_t[1] = 0.0;
#endif

  printf("%.6e %.6e %6e %.6e %.6e %.6e\n", tt_pre, plan.MEASURE_TIME_t[0], plan.MEASURE_TIME_t[1], plan.MEASURE_TIME_t[2], tt_total-tt_pre-plan.MEASURE_TIME_t[0]-plan.MEASURE_TIME_t[1]-plan.MEASURE_TIME_t[2], tt_total);

  /** finalise the one dimensional plan */
  nfsft_finalize(&plan);
}
Ejemplo n.º 5
0
/**
 * The main program.
 *
 * \param argc The number of arguments
 * \param argv An array containing the arguments as C-strings
 *
 * \return Exit code
 */
int main (int argc, char **argv)
{
  int tc;                      /**< The index variable for testcases          */
  int tc_max;                  /**< The number of testcases                   */

  int *NQ;                     /**< The array containing the cut-off degrees  *
                                    \f$N\f$                                   */
  int NQ_max;                  /**< The maximum cut-off degree \f$N\f$ for the*
                                    current testcase                          */
  int *SQ;                     /**< The array containing the grid size
                                    parameters                                */
  int SQ_max;                  /**< The maximum grid size parameter           */
  int *RQ;                     /**< The array containing the grid size
                                    parameters                                */
  int iNQ;                     /**< Index variable for cut-off degrees        */
  int iNQ_max;                 /**< The maximum number of cut-off degrees     */
  int testfunction;            /**< The testfunction                          */
  int N;                       /**< The test function's bandwidth             */

  int use_nfsft;               /**< Whether to use the NFSFT algorithm or not */
  int use_nfft;                /**< Whether to use the NFFT algorithm or not  */
  int use_fpt;                 /**< Whether to use the FPT algorithm or not   */
  int cutoff;                  /**< The current NFFT cut-off parameter        */
  double threshold;            /**< The current NFSFT threshold parameter     */

  int gridtype;                /**< The type of quadrature grid to be used    */
  int repetitions;             /**< The number of repetitions to be performed */
  int mode;                    /**< The number of repetitions to be performed */

  double *w;                   /**< The quadrature weights                    */
  double *x_grid;              /**< The quadrature nodes                      */
  double *x_compare;           /**< The quadrature nodes                      */
  double _Complex *f_grid;             /**< The reference function values             */
  double _Complex *f_compare;          /**< The function values                       */
  double _Complex *f;                  /**< The function values                       */
  double _Complex *f_hat_gen;         /**< The reference spherical Fourier           *
                                    coefficients                              */
  double _Complex *f_hat;              /**< The spherical Fourier coefficients        */

  nfsft_plan plan_adjoint;     /**< The NFSFT plan                            */
  nfsft_plan plan;             /**< The NFSFT plan                            */
  nfsft_plan plan_gen;         /**< The NFSFT plan                            */

  double t_avg;                /**< The average computation time needed       */
  double err_infty_avg;        /**< The average error \f$E_\infty\f$          */
  double err_2_avg;            /**< The average error \f$E_2\f$               */

  int i;                       /**< A loop variable                           */
  int k;                       /**< A loop variable                           */
  int n;                       /**< A loop variable                           */
  int d;                       /**< A loop variable                           */

  int m_theta;                 /**< The current number of different           *
                                    colatitudinal angles (for grids)          */
  int m_phi;                   /**< The current number of different           *
                                    longitudinal angles (for grids).          */
  int m_total;                 /**< The total number nodes.                   */
  double *theta;               /**< An array for saving the angles theta of a *
                                    grid                                      */
  double *phi;                 /**< An array for saving the angles phi of a   *
                                    grid                                      */
  fftw_plan fplan;             /**< An FFTW plan for computing Clenshaw-Curtis
                                    quadrature weights                        */
  //int nside;                   /**< The size parameter for the HEALPix grid   */
  int d2;
  int M;
  double theta_s;
  double x1,x2,x3,temp;
  int m_compare;
  nfsft_plan *plan_adjoint_ptr;
  nfsft_plan *plan_ptr;
  double *w_temp;
  int testmode;
  ticks t0, t1;

  /* Read the number of testcases. */
  fscanf(stdin,"testcases=%d\n",&tc_max);
  fprintf(stdout,"%d\n",tc_max);

  /* Process each testcase. */
  for (tc = 0; tc < tc_max; tc++)
  {
    /* Check if the fast transform shall be used. */
    fscanf(stdin,"nfsft=%d\n",&use_nfsft);
    fprintf(stdout,"%d\n",use_nfsft);
    if (use_nfsft != NO)
    {
      /* Check if the NFFT shall be used. */
      fscanf(stdin,"nfft=%d\n",&use_nfft);
      fprintf(stdout,"%d\n",use_nfsft);
      if (use_nfft != NO)
      {
        /* Read the cut-off parameter. */
        fscanf(stdin,"cutoff=%d\n",&cutoff);
        fprintf(stdout,"%d\n",cutoff);
      }
      else
      {
        /* TODO remove this */
        /* Initialize unused variable with dummy value. */
        cutoff = 1;
      }
      /* Check if the fast polynomial transform shall be used. */
      fscanf(stdin,"fpt=%d\n",&use_fpt);
      fprintf(stdout,"%d\n",use_fpt);
      if (use_fpt != NO)
      {
        /* Read the NFSFT threshold parameter. */
        fscanf(stdin,"threshold=%lf\n",&threshold);
        fprintf(stdout,"%lf\n",threshold);
      }
      else
      {
        /* TODO remove this */
        /* Initialize unused variable with dummy value. */
        threshold = 1000.0;
      }
    }
    else
    {
      /* TODO remove this */
      /* Set dummy values. */
      use_nfft = NO;
      use_fpt = NO;
      cutoff = 3;
      threshold = 1000.0;
    }

    /* Read the testmode type. */
    fscanf(stdin,"testmode=%d\n",&testmode);
    fprintf(stdout,"%d\n",testmode);

    if (testmode == ERROR)
    {
      /* Read the quadrature grid type. */
      fscanf(stdin,"gridtype=%d\n",&gridtype);
      fprintf(stdout,"%d\n",gridtype);

      /* Read the test function. */
      fscanf(stdin,"testfunction=%d\n",&testfunction);
      fprintf(stdout,"%d\n",testfunction);

      /* Check if random bandlimited function has been chosen. */
      if (testfunction == FUNCTION_RANDOM_BANDLIMITED)
      {
        /* Read the bandwidht. */
        fscanf(stdin,"bandlimit=%d\n",&N);
        fprintf(stdout,"%d\n",N);
      }
      else
      {
        N = 1;
      }

      /* Read the number of repetitions. */
      fscanf(stdin,"repetitions=%d\n",&repetitions);
      fprintf(stdout,"%d\n",repetitions);

      fscanf(stdin,"mode=%d\n",&mode);
      fprintf(stdout,"%d\n",mode);

      if (mode == RANDOM)
      {
        /* Read the bandwidht. */
        fscanf(stdin,"points=%d\n",&m_compare);
        fprintf(stdout,"%d\n",m_compare);
        x_compare = (double*) nfft_malloc(2*m_compare*sizeof(double));
        d = 0;
        while (d < m_compare)
        {
          x1 = 2.0*(((double)rand())/RAND_MAX) - 1.0;
          x2 = 2.0*(((double)rand())/RAND_MAX) - 1.0;
          x3 = 2.0*(((double)rand())/RAND_MAX) - 1.0;
          temp = sqrt(x1*x1+x2*x2+x3*x3);
          if (temp <= 1)
          {
            x_compare[2*d+1] = acos(x3);
            if (x_compare[2*d+1] == 0 || x_compare[2*d+1] == KPI)
            {
              x_compare[2*d] = 0.0;
            }
            else
            {
              x_compare[2*d] = atan2(x2/sin(x_compare[2*d+1]),x1/sin(x_compare[2*d+1]));
            }
            x_compare[2*d] *= 1.0/(2.0*KPI);
            x_compare[2*d+1] *= 1.0/(2.0*KPI);
            d++;
          }
        }
        f_compare = (double _Complex*) nfft_malloc(m_compare*sizeof(double _Complex));
        f = (double _Complex*) nfft_malloc(m_compare*sizeof(double _Complex));
      }
    }

    /* Initialize maximum cut-off degree and grid size parameter. */
    NQ_max = 0;
    SQ_max = 0;

    /* Read the number of cut-off degrees. */
    fscanf(stdin,"bandwidths=%d\n",&iNQ_max);
    fprintf(stdout,"%d\n",iNQ_max);

    /* Allocate memory for the cut-off degrees and grid size parameters. */
    NQ = (int*) nfft_malloc(iNQ_max*sizeof(int));
    SQ = (int*) nfft_malloc(iNQ_max*sizeof(int));
    if (testmode == TIMING)
    {
      RQ = (int*) nfft_malloc(iNQ_max*sizeof(int));
    }

    /* Read the cut-off degrees and grid size parameters. */
    for (iNQ = 0; iNQ < iNQ_max; iNQ++)
    {
      if (testmode == TIMING)
      {
        /* Read cut-off degree and grid size parameter. */
        fscanf(stdin,"%d %d %d\n",&NQ[iNQ],&SQ[iNQ],&RQ[iNQ]);
        fprintf(stdout,"%d %d %d\n",NQ[iNQ],SQ[iNQ],RQ[iNQ]);
        NQ_max = MAX(NQ_max,NQ[iNQ]);
        SQ_max = MAX(SQ_max,SQ[iNQ]);
      }
      else
      {
        /* Read cut-off degree and grid size parameter. */
        fscanf(stdin,"%d %d\n",&NQ[iNQ],&SQ[iNQ]);
        fprintf(stdout,"%d %d\n",NQ[iNQ],SQ[iNQ]);
        NQ_max = MAX(NQ_max,NQ[iNQ]);
        SQ_max = MAX(SQ_max,SQ[iNQ]);
      }
    }

    /* Do precomputation. */
    //fprintf(stderr,"NFSFT Precomputation\n");
    //fflush(stderr);
    nfsft_precompute(NQ_max, threshold,
      ((use_nfsft==NO)?(NFSFT_NO_FAST_ALGORITHM):(0U)), 0U);

    if (testmode == TIMING)
    {
      /* Allocate data structures. */
      f_hat = (double _Complex*) nfft_malloc(NFSFT_F_HAT_SIZE(NQ_max)*sizeof(double _Complex));
      f = (double _Complex*) nfft_malloc(SQ_max*sizeof(double _Complex));
      x_grid = (double*) nfft_malloc(2*SQ_max*sizeof(double));
      for (d = 0; d < SQ_max; d++)
      {
        f[d] = (((double)rand())/RAND_MAX)-0.5 + _Complex_I*((((double)rand())/RAND_MAX)-0.5);
        x_grid[2*d] = (((double)rand())/RAND_MAX) - 0.5;
        x_grid[2*d+1] = (((double)rand())/RAND_MAX) * 0.5;
      }
    }

    //fprintf(stderr,"Entering loop\n");
    //fflush(stderr);
    /* Process all cut-off bandwidths. */
    for (iNQ = 0; iNQ < iNQ_max; iNQ++)
    {
      if (testmode == TIMING)
      {
        nfsft_init_guru(&plan,NQ[iNQ],SQ[iNQ], NFSFT_NORMALIZED |
          ((use_nfft!=NO)?(0U):(NFSFT_USE_NDFT)) |
          ((use_fpt!=NO)?(0U):(NFSFT_USE_DPT)),
          PRE_PHI_HUT | PRE_PSI | FFTW_INIT | FFTW_MEASURE | FFT_OUT_OF_PLACE,
          cutoff);

        plan.f_hat = f_hat;
        plan.x = x_grid;
        plan.f = f;

        nfsft_precompute_x(&plan);

        t_avg = 0.0;

        for (i = 0; i < RQ[iNQ]; i++)
        {
          t0 = getticks();

          if (use_nfsft != NO)
          {
            /* Execute the adjoint NFSFT transformation. */
            nfsft_adjoint(&plan);
          }
          else
          {
            /* Execute the adjoint direct NDSFT transformation. */
            nfsft_adjoint_direct(&plan);
          }

          t1 = getticks();
          t_avg += nfft_elapsed_seconds(t1,t0);
        }

        t_avg = t_avg/((double)RQ[iNQ]);

        nfsft_finalize(&plan);

        fprintf(stdout,"%+le\n", t_avg);
        fprintf(stderr,"%d: %4d %4d %+le\n", tc, NQ[iNQ], SQ[iNQ], t_avg);
      }
      else
      {
        /* Determine the maximum number of nodes. */
        switch (gridtype)
        {
          case GRID_GAUSS_LEGENDRE:
            /* Calculate grid dimensions. */
            m_theta = SQ[iNQ] + 1;
            m_phi = 2*SQ[iNQ] + 2;
            m_total = m_theta*m_phi;
            break;
          case GRID_CLENSHAW_CURTIS:
            /* Calculate grid dimensions. */
            m_theta = 2*SQ[iNQ] + 1;
            m_phi = 2*SQ[iNQ] + 2;
            m_total = m_theta*m_phi;
            break;
          case GRID_HEALPIX:
            m_theta = 1;
            m_phi = 12*SQ[iNQ]*SQ[iNQ];
            m_total = m_theta * m_phi;
            //fprintf("HEALPix: SQ = %d, m_theta = %d, m_phi= %d, m");
            break;
          case GRID_EQUIDISTRIBUTION:
          case GRID_EQUIDISTRIBUTION_UNIFORM:
            m_theta = 2;
            //fprintf(stderr,"ed: m_theta = %d\n",m_theta);
            for (k = 1; k < SQ[iNQ]; k++)
            {
              m_theta += (int)floor((2*KPI)/acos((cos(KPI/(double)SQ[iNQ])-
                cos(k*KPI/(double)SQ[iNQ])*cos(k*KPI/(double)SQ[iNQ]))/
                (sin(k*KPI/(double)SQ[iNQ])*sin(k*KPI/(double)SQ[iNQ]))));
              //fprintf(stderr,"ed: m_theta = %d\n",m_theta);
            }
            //fprintf(stderr,"ed: m_theta final = %d\n",m_theta);
            m_phi = 1;
            m_total = m_theta * m_phi;
            break;
        }

        /* Allocate memory for data structures. */
        w = (double*) nfft_malloc(m_theta*sizeof(double));
        x_grid = (double*) nfft_malloc(2*m_total*sizeof(double));

        //fprintf(stderr,"NQ = %d\n",NQ[iNQ]);
        //fflush(stderr);
        switch (gridtype)
        {
          case GRID_GAUSS_LEGENDRE:
            //fprintf(stderr,"Generating grid for NQ = %d, SQ = %d\n",NQ[iNQ],SQ[iNQ]);
            //fflush(stderr);

            /* Read quadrature weights. */
            for (k = 0; k < m_theta; k++)
            {
              fscanf(stdin,"%le\n",&w[k]);
              w[k] *= (2.0*KPI)/((double)m_phi);
            }

            //fprintf(stderr,"Allocating theta and phi\n");
            //fflush(stderr);
            /* Allocate memory to store the grid's angles. */
            theta = (double*) nfft_malloc(m_theta*sizeof(double));
            phi = (double*) nfft_malloc(m_phi*sizeof(double));

            //if (theta == NULL || phi == NULL)
            //{
              //fprintf(stderr,"Couldn't allocate theta and phi\n");
              //fflush(stderr);
            //}


            /* Read angles theta. */
            for (k = 0; k < m_theta; k++)
            {
              fscanf(stdin,"%le\n",&theta[k]);
            }

            /* Generate the grid angles phi. */
            for (n = 0; n < m_phi; n++)
            {
              phi[n] = n/((double)m_phi);
              phi[n] -= ((phi[n]>=0.5)?(1.0):(0.0));
            }

            //fprintf(stderr,"Generating grid nodes\n");
            //fflush(stderr);

            /* Generate the grid's nodes. */
            d = 0;
            for (k = 0; k < m_theta; k++)
            {
              for (n = 0; n < m_phi; n++)
              {
                x_grid[2*d] = phi[n];
                x_grid[2*d+1] = theta[k];
                d++;
              }
            }

            //fprintf(stderr,"Freeing theta and phi\n");
            //fflush(stderr);
            /* Free the arrays for the grid's angles. */
            nfft_free(theta);
            nfft_free(phi);

            break;

          case GRID_CLENSHAW_CURTIS:

            /* Allocate memory to store the grid's angles. */
            theta = (double*) nfft_malloc(m_theta*sizeof(double));
            phi = (double*) nfft_malloc(m_phi*sizeof(double));

            /* Generate the grid angles theta. */
            for (k = 0; k < m_theta; k++)
            {
              theta[k] = k/((double)2*(m_theta-1));
            }

            /* Generate the grid angles phi. */
            for (n = 0; n < m_phi; n++)
            {
              phi[n] = n/((double)m_phi);
              phi[n] -= ((phi[n]>=0.5)?(1.0):(0.0));
            }

            /* Generate quadrature weights. */
            fplan = fftw_plan_r2r_1d(SQ[iNQ]+1, w, w, FFTW_REDFT00, 0U);
            for (k = 0; k < SQ[iNQ]+1; k++)
            {
              w[k] = -2.0/(4*k*k-1);
            }
            fftw_execute(fplan);
            w[0] *= 0.5;

            for (k = 0; k < SQ[iNQ]+1; k++)
            {
              w[k] *= (2.0*KPI)/((double)(m_theta-1)*m_phi);
              w[m_theta-1-k] = w[k];
            }
            fftw_destroy_plan(fplan);

            /* Generate the grid's nodes. */
            d = 0;
            for (k = 0; k < m_theta; k++)
            {
              for (n = 0; n < m_phi; n++)
              {
                x_grid[2*d] = phi[n];
                x_grid[2*d+1] = theta[k];
                d++;
              }
            }

            /* Free the arrays for the grid's angles. */
            nfft_free(theta);
            nfft_free(phi);

            break;

          case GRID_HEALPIX:

            d = 0;
            for (k = 1; k <= SQ[iNQ]-1; k++)
            {
              for (n = 0; n <= 4*k-1; n++)
              {
                x_grid[2*d+1] = 1 - (k*k)/((double)(3.0*SQ[iNQ]*SQ[iNQ]));
                x_grid[2*d] =  ((n+0.5)/(4*k));
                x_grid[2*d] -= (x_grid[2*d]>=0.5)?(1.0):(0.0);
                d++;
              }
            }

            d2 = d-1;

            for (k = SQ[iNQ]; k <= 3*SQ[iNQ]; k++)
            {
              for (n = 0; n <= 4*SQ[iNQ]-1; n++)
              {
                x_grid[2*d+1] = 2.0/(3*SQ[iNQ])*(2*SQ[iNQ]-k);
                x_grid[2*d] = (n+((k%2==0)?(0.5):(0.0)))/(4*SQ[iNQ]);
                x_grid[2*d] -= (x_grid[2*d]>=0.5)?(1.0):(0.0);
                d++;
              }
            }

            for (k = 1; k <= SQ[iNQ]-1; k++)
            {
              for (n = 0; n <= 4*k-1; n++)
              {
                x_grid[2*d+1] = -x_grid[2*d2+1];
                x_grid[2*d] =  x_grid[2*d2];
                d++;
                d2--;
              }
            }

            for (d = 0; d < m_total; d++)
            {
              x_grid[2*d+1] = acos(x_grid[2*d+1])/(2.0*KPI);
            }

            w[0] = (4.0*KPI)/(m_total);
            break;

          case GRID_EQUIDISTRIBUTION:
          case GRID_EQUIDISTRIBUTION_UNIFORM:
            /* TODO Compute the weights. */

            if (gridtype == GRID_EQUIDISTRIBUTION)
            {
              w_temp = (double*) nfft_malloc((SQ[iNQ]+1)*sizeof(double));
              fplan = fftw_plan_r2r_1d(SQ[iNQ]/2+1, w_temp, w_temp, FFTW_REDFT00, 0U);
              for (k = 0; k < SQ[iNQ]/2+1; k++)
              {
                w_temp[k] = -2.0/(4*k*k-1);
              }
              fftw_execute(fplan);
              w_temp[0] *= 0.5;

              for (k = 0; k < SQ[iNQ]/2+1; k++)
              {
                w_temp[k] *= (2.0*KPI)/((double)(SQ[iNQ]));
                w_temp[SQ[iNQ]-k] = w_temp[k];
              }
              fftw_destroy_plan(fplan);
            }

            d = 0;
            x_grid[2*d] = -0.5;
            x_grid[2*d+1] = 0.0;
            if (gridtype == GRID_EQUIDISTRIBUTION)
            {
              w[d] = w_temp[0];
            }
            else
            {
              w[d] = (4.0*KPI)/(m_total);
            }
            d = 1;
            x_grid[2*d] = -0.5;
            x_grid[2*d+1] = 0.5;
            if (gridtype == GRID_EQUIDISTRIBUTION)
            {
              w[d] = w_temp[SQ[iNQ]];
            }
            else
            {
              w[d] = (4.0*KPI)/(m_total);
            }
            d = 2;

            for (k = 1; k < SQ[iNQ]; k++)
            {
              theta_s = (double)k*KPI/(double)SQ[iNQ];
              M = (int)floor((2.0*KPI)/acos((cos(KPI/(double)SQ[iNQ])-
                cos(theta_s)*cos(theta_s))/(sin(theta_s)*sin(theta_s))));

              for (n = 0; n < M; n++)
              {
                x_grid[2*d] = (n + 0.5)/M;
                x_grid[2*d] -= (x_grid[2*d]>=0.5)?(1.0):(0.0);
                x_grid[2*d+1] = theta_s/(2.0*KPI);
                if (gridtype == GRID_EQUIDISTRIBUTION)
                {
                  w[d] = w_temp[k]/((double)(M));
                }
                else
                {
                  w[d] = (4.0*KPI)/(m_total);
                }
                d++;
              }
            }

            if (gridtype == GRID_EQUIDISTRIBUTION)
            {
              nfft_free(w_temp);
            }
            break;

          default:
            break;
        }

        /* Allocate memory for grid values. */
        f_grid = (double _Complex*) nfft_malloc(m_total*sizeof(double _Complex));

        if (mode == RANDOM)
        {
        }
        else
        {
          m_compare = m_total;
          f_compare = (double _Complex*) nfft_malloc(m_compare*sizeof(double _Complex));
          x_compare = x_grid;
          f = f_grid;
        }

        //fprintf(stderr,"Generating test function\n");
        //fflush(stderr);
        switch (testfunction)
        {
          case FUNCTION_RANDOM_BANDLIMITED:
            f_hat_gen = (double _Complex*) nfft_malloc(NFSFT_F_HAT_SIZE(N)*sizeof(double _Complex));
            //fprintf(stderr,"Generating random test function\n");
            //fflush(stderr);
            /* Generate random function samples by sampling a bandlimited
             * function. */
            nfsft_init_guru(&plan_gen,N,m_total, NFSFT_NORMALIZED |
              ((use_nfft!=NO)?(0U):(NFSFT_USE_NDFT)) |
              ((use_fpt!=NO)?(0U):(NFSFT_USE_DPT)),
              ((N>512)?(0U):(PRE_PHI_HUT | PRE_PSI)) | FFTW_INIT |
              FFT_OUT_OF_PLACE, cutoff);

            plan_gen.f_hat = f_hat_gen;
            plan_gen.x = x_grid;
            plan_gen.f = f_grid;

            nfsft_precompute_x(&plan_gen);

            for (k = 0; k < plan_gen.N_total; k++)
            {
              f_hat_gen[k] = 0.0;
            }

            for (k = 0; k <= N; k++)
            {
              for (n = -k; n <= k; n++)
              {
                f_hat_gen[NFSFT_INDEX(k,n,&plan_gen)] =
                (((double)rand())/RAND_MAX)-0.5 + _Complex_I*((((double)rand())/RAND_MAX)-0.5);
              }
            }

            if (use_nfsft != NO)
            {
              /* Execute the NFSFT transformation. */
              nfsft_trafo(&plan_gen);
            }
            else
            {
              /* Execute the direct NDSFT transformation. */
              nfsft_trafo_direct(&plan_gen);
            }

            nfsft_finalize(&plan_gen);

            if (mode == RANDOM)
            {
              nfsft_init_guru(&plan_gen,N,m_compare, NFSFT_NORMALIZED |
                ((use_nfft!=NO)?(0U):(NFSFT_USE_NDFT)) |
                ((use_fpt!=NO)?(0U):(NFSFT_USE_DPT)),
                ((N>512)?(0U):(PRE_PHI_HUT | PRE_PSI)) | FFTW_INIT |
                FFT_OUT_OF_PLACE, cutoff);

              plan_gen.f_hat = f_hat_gen;
              plan_gen.x = x_compare;
              plan_gen.f = f_compare;

              nfsft_precompute_x(&plan_gen);

              if (use_nfsft != NO)
              {
                /* Execute the NFSFT transformation. */
                nfsft_trafo(&plan_gen);
              }
              else
              {
                /* Execute the direct NDSFT transformation. */
                nfsft_trafo_direct(&plan_gen);
              }

              nfsft_finalize(&plan_gen);
            }
            else
            {
              memcpy(f_compare,f_grid,m_total*sizeof(double _Complex));
            }

            nfft_free(f_hat_gen);

            break;

          case FUNCTION_F1:
            for (d = 0; d < m_total; d++)
            {
              x1 = sin(x_grid[2*d+1]*2.0*KPI)*cos(x_grid[2*d]*2.0*KPI);
              x2 = sin(x_grid[2*d+1]*2.0*KPI)*sin(x_grid[2*d]*2.0*KPI);
              x3 = cos(x_grid[2*d+1]*2.0*KPI);
              f_grid[d] = x1*x2*x3;
            }
            if (mode == RANDOM)
            {
              for (d = 0; d < m_compare; d++)
              {
                x1 = sin(x_compare[2*d+1]*2.0*KPI)*cos(x_compare[2*d]*2.0*KPI);
                x2 = sin(x_compare[2*d+1]*2.0*KPI)*sin(x_compare[2*d]*2.0*KPI);
                x3 = cos(x_compare[2*d+1]*2.0*KPI);
                f_compare[d] = x1*x2*x3;
              }
            }
            else
            {
              memcpy(f_compare,f_grid,m_total*sizeof(double _Complex));
            }
            break;
          case FUNCTION_F2:
            for (d = 0; d < m_total; d++)
            {
              x1 = sin(x_grid[2*d+1]*2.0*KPI)*cos(x_grid[2*d]*2.0*KPI);
              x2 = sin(x_grid[2*d+1]*2.0*KPI)*sin(x_grid[2*d]*2.0*KPI);
              x3 = cos(x_grid[2*d+1]*2.0*KPI);
              f_grid[d] = 0.1*exp(x1+x2+x3);
            }
            if (mode == RANDOM)
            {
              for (d = 0; d < m_compare; d++)
              {
                x1 = sin(x_compare[2*d+1]*2.0*KPI)*cos(x_compare[2*d]*2.0*KPI);
                x2 = sin(x_compare[2*d+1]*2.0*KPI)*sin(x_compare[2*d]*2.0*KPI);
                x3 = cos(x_compare[2*d+1]*2.0*KPI);
                f_compare[d] = 0.1*exp(x1+x2+x3);
              }
            }
            else
            {
              memcpy(f_compare,f_grid,m_total*sizeof(double _Complex));
            }
            break;
          case FUNCTION_F3:
            for (d = 0; d < m_total; d++)
            {
              x1 = sin(x_grid[2*d+1]*2.0*KPI)*cos(x_grid[2*d]*2.0*KPI);
              x2 = sin(x_grid[2*d+1]*2.0*KPI)*sin(x_grid[2*d]*2.0*KPI);
              x3 = cos(x_grid[2*d+1]*2.0*KPI);
              temp = sqrt(x1*x1)+sqrt(x2*x2)+sqrt(x3*x3);
              f_grid[d] = 0.1*temp;
            }
            if (mode == RANDOM)
            {
              for (d = 0; d < m_compare; d++)
              {
                x1 = sin(x_compare[2*d+1]*2.0*KPI)*cos(x_compare[2*d]*2.0*KPI);
                x2 = sin(x_compare[2*d+1]*2.0*KPI)*sin(x_compare[2*d]*2.0*KPI);
                x3 = cos(x_compare[2*d+1]*2.0*KPI);
                temp = sqrt(x1*x1)+sqrt(x2*x2)+sqrt(x3*x3);
                f_compare[d] = 0.1*temp;
              }
            }
            else
            {
              memcpy(f_compare,f_grid,m_total*sizeof(double _Complex));
            }
            break;
          case FUNCTION_F4:
            for (d = 0; d < m_total; d++)
            {
              x1 = sin(x_grid[2*d+1]*2.0*KPI)*cos(x_grid[2*d]*2.0*KPI);
              x2 = sin(x_grid[2*d+1]*2.0*KPI)*sin(x_grid[2*d]*2.0*KPI);
              x3 = cos(x_grid[2*d+1]*2.0*KPI);
              temp = sqrt(x1*x1)+sqrt(x2*x2)+sqrt(x3*x3);
              f_grid[d] = 1.0/(temp);
            }
            if (mode == RANDOM)
            {
              for (d = 0; d < m_compare; d++)
              {
                x1 = sin(x_compare[2*d+1]*2.0*KPI)*cos(x_compare[2*d]*2.0*KPI);
                x2 = sin(x_compare[2*d+1]*2.0*KPI)*sin(x_compare[2*d]*2.0*KPI);
                x3 = cos(x_compare[2*d+1]*2.0*KPI);
                temp = sqrt(x1*x1)+sqrt(x2*x2)+sqrt(x3*x3);
                f_compare[d] = 1.0/(temp);
              }
            }
            else
            {
              memcpy(f_compare,f_grid,m_total*sizeof(double _Complex));
            }
            break;
          case FUNCTION_F5:
            for (d = 0; d < m_total; d++)
            {
              x1 = sin(x_grid[2*d+1]*2.0*KPI)*cos(x_grid[2*d]*2.0*KPI);
              x2 = sin(x_grid[2*d+1]*2.0*KPI)*sin(x_grid[2*d]*2.0*KPI);
              x3 = cos(x_grid[2*d+1]*2.0*KPI);
              temp = sqrt(x1*x1)+sqrt(x2*x2)+sqrt(x3*x3);
              f_grid[d] = 0.1*sin(1+temp)*sin(1+temp);
            }
            if (mode == RANDOM)
            {
              for (d = 0; d < m_compare; d++)
              {
                x1 = sin(x_compare[2*d+1]*2.0*KPI)*cos(x_compare[2*d]*2.0*KPI);
                x2 = sin(x_compare[2*d+1]*2.0*KPI)*sin(x_compare[2*d]*2.0*KPI);
                x3 = cos(x_compare[2*d+1]*2.0*KPI);
                temp = sqrt(x1*x1)+sqrt(x2*x2)+sqrt(x3*x3);
                f_compare[d] = 0.1*sin(1+temp)*sin(1+temp);
              }
            }
            else
            {
              memcpy(f_compare,f_grid,m_total*sizeof(double _Complex));
            }
            break;
          case FUNCTION_F6:
            for (d = 0; d < m_total; d++)
            {
              if (x_grid[2*d+1] <= 0.25)
              {
                f_grid[d] = 1.0;
              }
              else
              {
                f_grid[d] = 1.0/(sqrt(1+3*cos(2.0*KPI*x_grid[2*d+1])*cos(2.0*KPI*x_grid[2*d+1])));
              }
            }
            if (mode == RANDOM)
            {
              for (d = 0; d < m_compare; d++)
              {
                if (x_compare[2*d+1] <= 0.25)
                {
                  f_compare[d] = 1.0;
                }
                else
                {
                  f_compare[d] = 1.0/(sqrt(1+3*cos(2.0*KPI*x_compare[2*d+1])*cos(2.0*KPI*x_compare[2*d+1])));
                }
              }
            }
            else
            {
              memcpy(f_compare,f_grid,m_total*sizeof(double _Complex));
            }
            break;
          default:
            //fprintf(stderr,"Generating one function\n");
            //fflush(stderr);
            for (d = 0; d < m_total; d++)
            {
              f_grid[d] = 1.0;
            }
            if (mode == RANDOM)
            {
              for (d = 0; d < m_compare; d++)
              {
                f_compare[d] = 1.0;
              }
            }
            else
            {
              memcpy(f_compare,f_grid,m_total*sizeof(double _Complex));
            }
            break;
        }

        //fprintf(stderr,"Initializing trafo\n");
        //fflush(stderr);
        /* Init transform plan. */
        nfsft_init_guru(&plan_adjoint,NQ[iNQ],m_total, NFSFT_NORMALIZED |
          ((use_nfft!=NO)?(0U):(NFSFT_USE_NDFT)) |
          ((use_fpt!=NO)?(0U):(NFSFT_USE_DPT)),
          ((NQ[iNQ]>512)?(0U):(PRE_PHI_HUT | PRE_PSI)) | FFTW_INIT |
          FFT_OUT_OF_PLACE, cutoff);

        plan_adjoint_ptr = &plan_adjoint;

        if (mode == RANDOM)
        {
          nfsft_init_guru(&plan,NQ[iNQ],m_compare, NFSFT_NORMALIZED |
            ((use_nfft!=NO)?(0U):(NFSFT_USE_NDFT)) |
            ((use_fpt!=NO)?(0U):(NFSFT_USE_DPT)),
            ((NQ[iNQ]>512)?(0U):(PRE_PHI_HUT | PRE_PSI)) | FFTW_INIT |
            FFT_OUT_OF_PLACE, cutoff);
          plan_ptr = &plan;
        }
        else
        {
          plan_ptr = &plan_adjoint;
        }

        f_hat = (double _Complex*) nfft_malloc(NFSFT_F_HAT_SIZE(NQ[iNQ])*sizeof(double _Complex));

        plan_adjoint_ptr->f_hat = f_hat;
        plan_adjoint_ptr->x = x_grid;
        plan_adjoint_ptr->f = f_grid;

        plan_ptr->f_hat = f_hat;
        plan_ptr->x = x_compare;
        plan_ptr->f = f;

        //fprintf(stderr,"Precomputing for x\n");
        //fflush(stderr);
        nfsft_precompute_x(plan_adjoint_ptr);
        if (plan_adjoint_ptr != plan_ptr)
        {
          nfsft_precompute_x(plan_ptr);
        }

        /* Initialize cumulative time variable. */
        t_avg = 0.0;
        err_infty_avg = 0.0;
        err_2_avg = 0.0;

        /* Cycle through all runs. */
        for (i = 0; i < 1/*repetitions*/; i++)
        {
          //fprintf(stderr,"Copying original values\n");
          //fflush(stderr);
          /* Copy exact funtion values to working array. */
          //memcpy(f,f_grid,m_total*sizeof(double _Complex));

          /* Initialize time measurement. */
          t0 = getticks();

          //fprintf(stderr,"Multiplying with quadrature weights\n");
          //fflush(stderr);
          /* Multiplication with the quadrature weights. */
          /*fprintf(stderr,"\n");*/
          d = 0;
          for (k = 0; k < m_theta; k++)
          {
            for (n = 0; n < m_phi; n++)
            {
              /*fprintf(stderr,"f_ref[%d] = %le + I*%le,\t f[%d] = %le + I*%le,  \t w[%d] = %le\n",
              d,creal(f_ref[d]),cimag(f_ref[d]),d,creal(f[d]),cimag(f[d]),k,
              w[k]);*/
              f_grid[d] *= w[k];
              d++;
            }
          }

          t1 = getticks();
          t_avg += nfft_elapsed_seconds(t1,t0);

          nfft_free(w);

          t0 = getticks();

          /*fprintf(stderr,"\n");
          d = 0;
          for (d = 0; d < grid_total; d++)
          {
            fprintf(stderr,"f[%d] = %le + I*%le, theta[%d] = %le, phi[%d] = %le\n",
                    d,creal(f[d]),cimag(f[d]),d,x[2*d+1],d,x[2*d]);
          }*/

          //fprintf(stderr,"Executing adjoint\n");
          //fflush(stderr);
          /* Check if the fast NFSFT algorithm shall be tested. */
          if (use_nfsft != NO)
          {
            /* Execute the adjoint NFSFT transformation. */
            nfsft_adjoint(plan_adjoint_ptr);
          }
          else
          {
            /* Execute the adjoint direct NDSFT transformation. */
            nfsft_adjoint_direct(plan_adjoint_ptr);
          }

          /* Multiplication with the Fourier-Legendre coefficients. */
          /*for (k = 0; k <= m[im]; k++)
          {
            for (n = -k; n <= k; n++)
            {
              fprintf(stderr,"f_hat[%d,%d] = %le\t + I*%le\n",k,n,
                      creal(f_hat[NFSFT_INDEX(k,n,&plan_adjoint)]),
                      cimag(f_hat[NFSFT_INDEX(k,n,&plan_adjoint)]));
            }
          }*/

          //fprintf(stderr,"Executing trafo\n");
          //fflush(stderr);
          if (use_nfsft != NO)
          {
            /* Execute the NFSFT transformation. */
            nfsft_trafo(plan_ptr);
          }
          else
          {
            /* Execute the direct NDSFT transformation. */
            nfsft_trafo_direct(plan_ptr);
          }

          t1 = getticks();
          t_avg += nfft_elapsed_seconds(t1,t0);

          //fprintf(stderr,"Finalizing\n");
          //fflush(stderr);
          /* Finalize the NFSFT plans */
          nfsft_finalize(plan_adjoint_ptr);
          if (plan_ptr != plan_adjoint_ptr)
          {
            nfsft_finalize(plan_ptr);
          }

          /* Free data arrays. */
          nfft_free(f_hat);
          nfft_free(x_grid);

          err_infty_avg += X(error_l_infty_complex)(f, f_compare, m_compare);
          err_2_avg += X(error_l_2_complex)(f, f_compare, m_compare);

          nfft_free(f_grid);

          if (mode == RANDOM)
          {
          }
          else
          {
            nfft_free(f_compare);
          }

          /*for (d = 0; d < m_total; d++)
          {
            fprintf(stderr,"f_ref[%d] = %le + I*%le,\t f[%d] = %le + I*%le\n",
              d,creal(f_ref[d]),cimag(f_ref[d]),d,creal(f[d]),cimag(f[d]));
          }*/
        }

        //fprintf(stderr,"Calculating the error\n");
        //fflush(stderr);
        /* Calculate average time needed. */
        t_avg = t_avg/((double)repetitions);

        /* Calculate the average error. */
        err_infty_avg = err_infty_avg/((double)repetitions);

        /* Calculate the average error. */
        err_2_avg = err_2_avg/((double)repetitions);

        /* Print out the error measurements. */
        fprintf(stdout,"%+le %+le %+le\n", t_avg, err_infty_avg, err_2_avg);
        fprintf(stderr,"%d: %4d %4d %+le %+le %+le\n", tc, NQ[iNQ], SQ[iNQ],
          t_avg, err_infty_avg, err_2_avg);
      }
    } /* for (im = 0; im < im_max; im++) - Process all cut-off
       * bandwidths.*/
    fprintf(stderr,"\n");

    /* Delete precomputed data. */
    nfsft_forget();

    /* Free memory for cut-off bandwidths and grid size parameters. */
    nfft_free(NQ);
    nfft_free(SQ);
    if (testmode == TIMING)
    {
      nfft_free(RQ);
    }

    if (mode == RANDOM)
    {
      nfft_free(x_compare);
      nfft_free(f_compare);
      nfft_free(f);
    }

    if (testmode == TIMING)
    {
      /* Allocate data structures. */
      nfft_free(f_hat);
      nfft_free(f);
      nfft_free(x_grid);
    }

  } /* for (tc = 0; tc < tc_max; tc++) - Process each testcase. */

  /* Return exit code for successful run. */
  return EXIT_SUCCESS;
}
Ejemplo n.º 6
0
static void simple_test_nfsft(void)
{
  const int N = 4; /* bandwidth/maximum degree */
  const int M = 8; /* number of nodes */
  nfsft_plan plan; /* transform plan */
  int j, k, n; /* loop variables */

  /* precomputation (for fast polynomial transform) */
  nfsft_precompute(N,1000.0,0U,0U);

  /* Initialize transform plan using the guru interface. All input and output
   * arrays are allocated by nfsft_init_guru(). Computations are performed with
   * respect to L^2-normalized spherical harmonics Y_k^n. The array of spherical
   * Fourier coefficients is preserved during transformations. The NFFT uses a
   * cut-off parameter m = 6. See the NFFT 3 manual for details.
   */
  nfsft_init_guru(&plan, N, M, NFSFT_MALLOC_X | NFSFT_MALLOC_F |
    NFSFT_MALLOC_F_HAT | NFSFT_NORMALIZED | NFSFT_PRESERVE_F_HAT,
    PRE_PHI_HUT | PRE_PSI | FFTW_INIT | FFT_OUT_OF_PLACE, 6);

  /* pseudo-random nodes */
  for (j = 0; j < plan.M_total; j++)
  {
    plan.x[2*j]= nfft_drand48() - K(0.5);
    plan.x[2*j+1]= K(0.5) * nfft_drand48();
  }

  /* precomputation (for NFFT, node-dependent) */
  nfsft_precompute_x(&plan);

  /* pseudo-random Fourier coefficients */
  for (k = 0; k <= plan.N; k++)
    for (n = -k; n <= k; n++)
      plan.f_hat[NFSFT_INDEX(k,n,&plan)] =
          nfft_drand48() - K(0.5) + _Complex_I*(nfft_drand48() - K(0.5));

  /* Direct transformation, display result. */
  nfsft_trafo_direct(&plan);
  printf("Vector f (NDSFT):\n");
  for (j = 0; j < plan.M_total; j++)
    printf("f[%+2d] = %+5.3" __FES__ " %+5.3" __FES__ "*I\n",j,
      creal(plan.f[j]), cimag(plan.f[j]));

  printf("\n");

  /* Fast approximate transformation, display result. */
  nfsft_trafo(&plan);
  printf("Vector f (NFSFT):\n");
  for (j = 0; j < plan.M_total; j++)
    printf("f[%+2d] = %+5.3" __FES__ " %+5.3" __FES__ "*I\n",j,
      creal(plan.f[j]), cimag(plan.f[j]));

  printf("\n");

  /* Direct adjoint transformation, display result. */
  nfsft_adjoint_direct(&plan);
  printf("Vector f_hat (NDSFT):\n");
  for (k = 0; k <= plan.N; k++)
    for (n = -k; n <= k; n++)
      fprintf(stdout,"f_hat[%+2d,%+2d] = %+5.3" __FES__ " %+5.3" __FES__ "*I\n",k,n,
        creal(plan.f_hat[NFSFT_INDEX(k,n,&plan)]),
        cimag(plan.f_hat[NFSFT_INDEX(k,n,&plan)]));

  printf("\n");

  /* Fast approximate adjoint transformation, display result. */
  nfsft_adjoint(&plan);
  printf("Vector f_hat (NFSFT):\n");
  for (k = 0; k <= plan.N; k++)
  {
    for (n = -k; n <= k; n++)
    {
      fprintf(stdout,"f_hat[%+2d,%+2d] = %+5.3" __FES__ " %+5.3" __FES__ "*I\n",k,n,
        creal(plan.f_hat[NFSFT_INDEX(k,n,&plan)]),
        cimag(plan.f_hat[NFSFT_INDEX(k,n,&plan)]));
    }
  }

  /* Finalize the plan. */
  nfsft_finalize(&plan);

  /* Destroy data precomputed for fast polynomial transform. */
	nfsft_forget();
}
Ejemplo n.º 7
0
/**
 * The main program.
 *
 * \param argc The number of arguments
 * \param argv An array containing the arguments as C-strings
 *
 * \return Exit code
 *
 * \author Jens Keiner
 */
int main (int argc, char **argv)
{
  double **p;                  /* The array containing the parameter sets     *
                                * for the kernel functions                    */
  int *m;                      /* The array containing the cut-off degrees M  */
  int **ld;                    /* The array containing the numbers of source  *
                                * and target nodes, L and D                   */
  int ip;                      /* Index variable for p                        */
  int im;                      /* Index variable for m                        */
  int ild;                     /* Index variable for l                        */
  int ipp;                     /* Index for kernel parameters                 */
  int ip_max;                  /* The maximum index for p                     */
  int im_max;                  /* The maximum index for m                     */
  int ild_max;                 /* The maximum index for l                     */
  int ipp_max;                 /* The maximum index for ip                    */
  int tc_max;                  /* The number of testcases                     */
  int m_max;                   /* The maximum cut-off degree M for the        *
                                * current dataset                             */
  int l_max;                   /* The maximum number of source nodes L for    *
                                * the current dataset                         */
  int d_max;                   /* The maximum number of target nodes D for    *
                                * the current dataset                         */
  long ld_max_prec;            /* The maximum number of source and target     *
                                * nodes for precomputation multiplied         */
  long l_max_prec;             /* The maximum number of source nodes for      *
                                * precomputation                              */
  int tc;                      /* Index variable for testcases                */
  int kt;                      /* The kernel function                         */
  int cutoff;                  /* The current NFFT cut-off parameter          */
  double threshold;            /* The current NFSFT threshold parameter       */
  double t_d;                  /* Time for direct algorithm in seconds        */
  double t_dp;                 /* Time for direct algorithm with              *
                                  precomputation in seconds                   */
  double t_fd;                 /* Time for fast direct algorithm in seconds   */
  double t_f;                  /* Time for fast algorithm in seconds          */
  double temp;                 /*                                             */
  double err_f;                /* Error E_infty for fast algorithm            */
  double err_fd;               /* Error E_\infty for fast direct algorithm    */
  ticks t0, t1;                /*                                             */
  int precompute = NO;         /*                                             */
  fftw_complex *ptr;         /*                                             */
  double* steed;               /*                                             */
  fftw_complex *b;           /* The weights (b_l)_{l=0}^{L-1}               */
  fftw_complex *f_hat;       /* The spherical Fourier coefficients          */
  fftw_complex *a;           /* The Fourier-Legendre coefficients           */
  double *xi;                  /* Target nodes                                */
  double *eta;                 /* Source nodes                                */
  fftw_complex *f_m;         /* Approximate function values                 */
  fftw_complex *f;           /* Exact function values                       */
  fftw_complex *prec = NULL; /*                                             */
  nfsft_plan plan;             /* NFSFT plan                                  */
  nfsft_plan plan_adjoint;     /* adjoint NFSFT plan                          */
  int i;                       /*                                             */
  int k;                       /*                                             */
  int n;                       /*                                             */
  int d;                       /*                                             */
  int l;                       /*                                             */
  int use_nfsft;               /*                                             */
  int use_nfft;                /*                                             */
  int use_fpt;                 /*                                             */
  int rinc;                    /*                                             */
  double constant;             /*                                             */

  /* Read the number of testcases. */
  fscanf(stdin,"testcases=%d\n",&tc_max);
  fprintf(stdout,"%d\n",tc_max);

  /* Process each testcase. */
  for (tc = 0; tc < tc_max; tc++)
  {
    /* Check if the fast transform shall be used. */
    fscanf(stdin,"nfsft=%d\n",&use_nfsft);
    fprintf(stdout,"%d\n",use_nfsft);
    if (use_nfsft != NO)
    {
      /* Check if the NFFT shall be used. */
      fscanf(stdin,"nfft=%d\n",&use_nfft);
      fprintf(stdout,"%d\n",use_nfft);
      if (use_nfft != NO)
      {
        /* Read the cut-off parameter. */
        fscanf(stdin,"cutoff=%d\n",&cutoff);
        fprintf(stdout,"%d\n",cutoff);
      }
      else
      {
        /* TODO remove this */
        /* Initialize unused variable with dummy value. */
        cutoff = 1;
      }
      /* Check if the fast polynomial transform shall be used. */
      fscanf(stdin,"fpt=%d\n",&use_fpt);
      fprintf(stdout,"%d\n",use_fpt);
      /* Read the NFSFT threshold parameter. */
      fscanf(stdin,"threshold=%lf\n",&threshold);
      fprintf(stdout,"%lf\n",threshold);
    }
    else
    {
      /* TODO remove this */
      /* Set dummy values. */
      cutoff = 3;
      threshold = 1000000000000.0;
    }

    /* Initialize bandwidth bound. */
    m_max = 0;
    /* Initialize source nodes bound. */
    l_max = 0;
    /* Initialize target nodes bound. */
    d_max = 0;
    /* Initialize source nodes bound for precomputation. */
    l_max_prec = 0;
    /* Initialize source and target nodes bound for precomputation. */
    ld_max_prec = 0;

    /* Read the kernel type. This is one of KT_ABEL_POISSON, KT_SINGULARITY,
     * KT_LOC_SUPP and KT_GAUSSIAN. */
    fscanf(stdin,"kernel=%d\n",&kt);
    fprintf(stdout,"%d\n",kt);

    /* Read the number of parameter sets. */
    fscanf(stdin,"parameter_sets=%d\n",&ip_max);
    fprintf(stdout,"%d\n",ip_max);

    /* Allocate memory for pointers to parameter sets. */
    p = (double**) nfft_malloc(ip_max*sizeof(double*));

    /* We now read in the parameter sets. */

    /* Read number of parameters. */
    fscanf(stdin,"parameters=%d\n",&ipp_max);
    fprintf(stdout,"%d\n",ipp_max);

    for (ip = 0; ip < ip_max; ip++)
    {
      /* Allocate memory for the parameters. */
      p[ip] = (double*) nfft_malloc(ipp_max*sizeof(double));

      /* Read the parameters. */
      for (ipp = 0; ipp < ipp_max; ipp++)
      {
        /* Read the next parameter. */
        fscanf(stdin,"%lf\n",&p[ip][ipp]);
        fprintf(stdout,"%lf\n",p[ip][ipp]);
      }
    }

    /* Read the number of cut-off degrees. */
    fscanf(stdin,"bandwidths=%d\n",&im_max);
    fprintf(stdout,"%d\n",im_max);
    m = (int*) nfft_malloc(im_max*sizeof(int));

    /* Read the cut-off degrees. */
    for (im = 0; im < im_max; im++)
    {
      /* Read cut-off degree. */
      fscanf(stdin,"%d\n",&m[im]);
      fprintf(stdout,"%d\n",m[im]);
      m_max = MAX(m_max,m[im]);
    }

    /* Read number of node specifications. */
    fscanf(stdin,"node_sets=%d\n",&ild_max);
    fprintf(stdout,"%d\n",ild_max);
    ld = (int**) nfft_malloc(ild_max*sizeof(int*));

    /* Read the run specification. */
    for (ild = 0; ild < ild_max; ild++)
    {
      /* Allocate memory for the run parameters. */
      ld[ild] = (int*) nfft_malloc(5*sizeof(int));

      /* Read number of source nodes. */
      fscanf(stdin,"L=%d ",&ld[ild][0]);
      fprintf(stdout,"%d\n",ld[ild][0]);
      l_max = MAX(l_max,ld[ild][0]);

      /* Read number of target nodes. */
      fscanf(stdin,"D=%d ",&ld[ild][1]);
      fprintf(stdout,"%d\n",ld[ild][1]);
      d_max = MAX(d_max,ld[ild][1]);

      /* Determine whether direct and fast algorithm shall be compared. */
      fscanf(stdin,"compare=%d ",&ld[ild][2]);
      fprintf(stdout,"%d\n",ld[ild][2]);

      /* Check if precomputation for the direct algorithm is used. */
      if (ld[ild][2] == YES)
      {
        /* Read whether the precomputed version shall also be used. */
        fscanf(stdin,"precomputed=%d\n",&ld[ild][3]);
        fprintf(stdout,"%d\n",ld[ild][3]);

        /* Read the number of repetitions over which measurements are
         * averaged. */
        fscanf(stdin,"repetitions=%d\n",&ld[ild][4]);
        fprintf(stdout,"%d\n",ld[ild][4]);

        /* Update ld_max_prec and l_max_prec. */
        if (ld[ild][3] == YES)
        {
          /* Update ld_max_prec. */
          ld_max_prec = MAX(ld_max_prec,ld[ild][0]*ld[ild][1]);
          /* Update l_max_prec. */
          l_max_prec = MAX(l_max_prec,ld[ild][0]);
          /* Turn on the precomputation for the direct algorithm. */
          precompute = YES;
        }
      }
      else
      {
        /* Set default value for the number of repetitions. */
        ld[ild][4] = 1;
      }
    }

    /* Allocate memory for data structures. */
    b = (fftw_complex*) nfft_malloc(l_max*sizeof(fftw_complex));
    eta = (double*) nfft_malloc(2*l_max*sizeof(double));
    f_hat = (fftw_complex*) nfft_malloc(NFSFT_F_HAT_SIZE(m_max)*sizeof(fftw_complex));
    a = (fftw_complex*) nfft_malloc((m_max+1)*sizeof(fftw_complex));
    xi = (double*) nfft_malloc(2*d_max*sizeof(double));
    f_m = (fftw_complex*) nfft_malloc(d_max*sizeof(fftw_complex));
    f = (fftw_complex*) nfft_malloc(d_max*sizeof(fftw_complex));

    /* Allocate memory for precomputed data. */
    if (precompute == YES)
    {
      prec = (fftw_complex*) nfft_malloc(ld_max_prec*sizeof(fftw_complex));
    }

    /* Generate random source nodes and weights. */
    for (l = 0; l < l_max; l++)
    {
      b[l] = (((double)rand())/RAND_MAX) - 0.5;
      eta[2*l] = (((double)rand())/RAND_MAX) - 0.5;
      eta[2*l+1] = acos(2.0*(((double)rand())/RAND_MAX) - 1.0)/(K2PI);
    }

    /* Generate random target nodes. */
    for (d = 0; d < d_max; d++)
    {
      xi[2*d] = (((double)rand())/RAND_MAX) - 0.5;
      xi[2*d+1] = acos(2.0*(((double)rand())/RAND_MAX) - 1.0)/(K2PI);
    }

    /* Do precomputation. */
    nfsft_precompute(m_max,threshold,
      ((use_nfsft==NO)?(NFSFT_NO_FAST_ALGORITHM):(0U/*NFSFT_NO_DIRECT_ALGORITHM*/)), 0U);

    /* Process all parameter sets. */
    for (ip = 0; ip < ip_max; ip++)
    {
      /* Compute kernel coeffcients up to the maximum cut-off degree m_max. */
      switch (kt)
      {
        case KT_ABEL_POISSON:
          /* Compute Fourier-Legendre coefficients for the Poisson kernel. */
          for (k = 0; k <= m_max; k++)
            a[k] = SYMBOL_ABEL_POISSON(k,p[ip][0]);
          break;

        case KT_SINGULARITY:
          /* Compute Fourier-Legendre coefficients for the singularity
           * kernel. */
          for (k = 0; k <= m_max; k++)
            a[k] = SYMBOL_SINGULARITY(k,p[ip][0]);
          break;

        case KT_LOC_SUPP:
          /* Compute Fourier-Legendre coefficients for the locally supported
           * kernel. */
          a[0] = 1.0;
          if (1 <= m_max)
            a[1] = ((p[ip][1]+1+p[ip][0])/(p[ip][1]+2.0))*a[0];
          for (k = 2; k <= m_max; k++)
            a[k] = (1.0/(k+p[ip][1]+1))*((2*k-1)*p[ip][0]*a[k-1] -
              (k-p[ip][1]-2)*a[k-2]);
          break;

        case KT_GAUSSIAN:
          /* Fourier-Legendre coefficients */
          steed = (double*) nfft_malloc((m_max+1)*sizeof(double));
          smbi(2.0*p[ip][0],0.5,m_max+1,2,steed);
          for (k = 0; k <= m_max; k++)
            a[k] = K2PI*(sqrt(KPI/p[ip][0]))*steed[k];

          nfft_free(steed);
          break;
      }

      /* Normalize Fourier-Legendre coefficients. */
      for (k = 0; k <= m_max; k++)
        a[k] *= (2*k+1)/(K4PI);

      /* Process all node sets. */
      for (ild = 0; ild < ild_max; ild++)
      {
        /* Check if the fast algorithm shall be used. */
        if (ld[ild][2] != NO)
        {
          /* Check if the direct algorithm with precomputation should be
           * tested. */
          if (ld[ild][3] != NO)
          {
            /* Get pointer to start of data. */
            ptr = prec;
            /* Calculate increment from one row to the next. */
            rinc = l_max_prec-ld[ild][0];

            /* Process al target nodes. */
            for (d = 0; d < ld[ild][1]; d++)
            {
              /* Process all source nodes. */
              for (l = 0; l < ld[ild][0]; l++)
              {
                /* Compute inner product between current source and target
                 * node. */
                temp = innerProduct(eta[2*l],eta[2*l+1],xi[2*d],xi[2*d+1]);

                /* Switch by the kernel type. */
                switch (kt)
                {
                  case KT_ABEL_POISSON:
                    /* Evaluate the Poisson kernel for the current value. */
                    *ptr++ = poissonKernel(temp,p[ip][0]);
                   break;

                  case KT_SINGULARITY:
                    /* Evaluate the singularity kernel for the current
                     * value. */
                    *ptr++ = singularityKernel(temp,p[ip][0]);
                    break;

                  case KT_LOC_SUPP:
                     /* Evaluate the localized kernel for the current
                      * value. */
                    *ptr++ = locallySupportedKernel(temp,p[ip][0],p[ip][1]);
                    break;

                    case KT_GAUSSIAN:
                       /* Evaluate the spherical Gaussian kernel for the current
                        * value. */
                      *ptr++ = gaussianKernel(temp,p[ip][0]);
                       break;
                }
              }
              /* Increment pointer for next row. */
              ptr += rinc;
            }

            /* Initialize cumulative time variable. */
            t_dp = 0.0;

            /* Initialize time measurement. */
            t0 = getticks();

            /* Cycle through all runs. */
            for (i = 0; i < ld[ild][4]; i++)
            {

              /* Reset pointer to start of precomputed data. */
              ptr = prec;
              /* Calculate increment from one row to the next. */
              rinc = l_max_prec-ld[ild][0];

              /* Check if the localized kernel is used. */
              if (kt == KT_LOC_SUPP)
              {
                /* Perform final summation */

                /* Calculate the multiplicative constant. */
                constant = ((p[ip][1]+1)/(K2PI*pow(1-p[ip][0],p[ip][1]+1)));

                /* Process all target nodes. */
                for (d = 0; d < ld[ild][1]; d++)
                {
                  /* Initialize function value. */
                  f[d] = 0.0;

                  /* Process all source nodes. */
                  for (l = 0; l < ld[ild][0]; l++)
                    f[d] += b[l]*(*ptr++);

                  /* Multiply with the constant. */
                  f[d] *= constant;

                  /* Proceed to next row. */
                  ptr += rinc;
                }
              }
              else
              {
                /* Process all target nodes. */
                for (d = 0; d < ld[ild][1]; d++)
                {
                  /* Initialize function value. */
                  f[d] = 0.0;

                  /* Process all source nodes. */
                  for (l = 0; l < ld[ild][0]; l++)
                    f[d] += b[l]*(*ptr++);

                  /* Proceed to next row. */
                  ptr += rinc;
                }
              }
            }

            /* Calculate the time needed. */
            t1 = getticks();
            t_dp = nfft_elapsed_seconds(t1,t0);

            /* Calculate average time needed. */
            t_dp = t_dp/((double)ld[ild][4]);
          }
          else
          {
            /* Initialize cumulative time variable with dummy value. */
            t_dp = -1.0;
          }

          /* Initialize cumulative time variable. */
          t_d = 0.0;

          /* Initialize time measurement. */
          t0 = getticks();

          /* Cycle through all runs. */
          for (i = 0; i < ld[ild][4]; i++)
          {
            /* Switch by the kernel type. */
            switch (kt)
            {
              case KT_ABEL_POISSON:

                /* Process all target nodes. */
                for (d = 0; d < ld[ild][1]; d++)
                {
                  /* Initialize function value. */
                  f[d] = 0.0;

                  /* Process all source nodes. */
                  for (l = 0; l < ld[ild][0]; l++)
                  {
                    /* Compute the inner product for the current source and
                     * target nodes. */
                    temp = innerProduct(eta[2*l],eta[2*l+1],xi[2*d],xi[2*d+1]);

                    /* Evaluate the Poisson kernel for the current value and add
                     * to the result. */
                    f[d] += b[l]*poissonKernel(temp,p[ip][0]);
                  }
                }
                break;

              case KT_SINGULARITY:
                /* Process all target nodes. */
                for (d = 0; d < ld[ild][1]; d++)
                {
                  /* Initialize function value. */
                  f[d] = 0.0;

                  /* Process all source nodes. */
                  for (l = 0; l < ld[ild][0]; l++)
                  {
                    /* Compute the inner product for the current source and
                     * target nodes. */
                    temp = innerProduct(eta[2*l],eta[2*l+1],xi[2*d],xi[2*d+1]);

                    /* Evaluate the Poisson kernel for the current value and add
                     * to the result. */
                    f[d] += b[l]*singularityKernel(temp,p[ip][0]);
                  }
                }
                break;

              case KT_LOC_SUPP:
                /* Calculate the multiplicative constant. */
                constant = ((p[ip][1]+1)/(K2PI*pow(1-p[ip][0],p[ip][1]+1)));

                /* Process all target nodes. */
                for (d = 0; d < ld[ild][1]; d++)
                {
                  /* Initialize function value. */
                  f[d] = 0.0;

                  /* Process all source nodes. */
                  for (l = 0; l < ld[ild][0]; l++)
                  {
                    /* Compute the inner product for the current source and
                     * target nodes. */
                    temp = innerProduct(eta[2*l],eta[2*l+1],xi[2*d],xi[2*d+1]);

                    /* Evaluate the Poisson kernel for the current value and add
                     * to the result. */
                    f[d] += b[l]*locallySupportedKernel(temp,p[ip][0],p[ip][1]);
                  }

                  /* Multiply result with constant. */
                  f[d] *= constant;
                }
                break;

                case KT_GAUSSIAN:
                  /* Process all target nodes. */
                  for (d = 0; d < ld[ild][1]; d++)
                  {
                    /* Initialize function value. */
                    f[d] = 0.0;

                    /* Process all source nodes. */
                    for (l = 0; l < ld[ild][0]; l++)
                    {
                      /* Compute the inner product for the current source and
                       * target nodes. */
                      temp = innerProduct(eta[2*l],eta[2*l+1],xi[2*d],xi[2*d+1]);
                      /* Evaluate the Poisson kernel for the current value and add
                       * to the result. */
                      f[d] += b[l]*gaussianKernel(temp,p[ip][0]);
                    }
                  }
                  break;
            }
          }

          /* Calculate and add the time needed. */
          t1 = getticks();
          t_d = nfft_elapsed_seconds(t1,t0);
          /* Calculate average time needed. */
          t_d = t_d/((double)ld[ild][4]);
        }
        else
        {
          /* Initialize cumulative time variable with dummy value. */
          t_d = -1.0;
          t_dp = -1.0;
        }

        /* Initialize error and cumulative time variables for the fast
         * algorithm. */
        err_fd = -1.0;
        err_f = -1.0;
        t_fd = -1.0;
        t_f = -1.0;

        /* Process all cut-off bandwidths. */
        for (im = 0; im < im_max; im++)
        {
          /* Init transform plans. */
          nfsft_init_guru(&plan_adjoint, m[im],ld[ild][0],
            ((use_nfft!=0)?(0U):(NFSFT_USE_NDFT)) |
            ((use_fpt!=0)?(0U):(NFSFT_USE_DPT)),
            PRE_PHI_HUT | PRE_PSI | FFTW_INIT |
            FFT_OUT_OF_PLACE, cutoff);
          nfsft_init_guru(&plan,m[im],ld[ild][1],
            ((use_nfft!=0)?(0U):(NFSFT_USE_NDFT)) |
            ((use_fpt!=0)?(0U):(NFSFT_USE_DPT)),
            PRE_PHI_HUT | PRE_PSI | FFTW_INIT |
            FFT_OUT_OF_PLACE,
             cutoff);
          plan_adjoint.f_hat = f_hat;
          plan_adjoint.x = eta;
          plan_adjoint.f = b;
          plan.f_hat = f_hat;
          plan.x = xi;
          plan.f = f_m;
          nfsft_precompute_x(&plan_adjoint);
          nfsft_precompute_x(&plan);

          /* Check if direct algorithm shall also be tested. */
          if (use_nfsft == BOTH)
          {
            /* Initialize cumulative time variable. */
            t_fd = 0.0;

            /* Initialize time measurement. */
            t0 = getticks();

            /* Cycle through all runs. */
            for (i = 0; i < ld[ild][4]; i++)
            {

              /* Execute adjoint direct NDSFT transformation. */
              nfsft_adjoint_direct(&plan_adjoint);

              /* Multiplication with the Fourier-Legendre coefficients. */
              for (k = 0; k <= m[im]; k++)
                for (n = -k; n <= k; n++)
                  f_hat[NFSFT_INDEX(k,n,&plan_adjoint)] *= a[k];

              /* Execute direct NDSFT transformation. */
              nfsft_trafo_direct(&plan);

            }

            /* Calculate and add the time needed. */
            t1 = getticks();
            t_fd = nfft_elapsed_seconds(t1,t0);

            /* Calculate average time needed. */
            t_fd = t_fd/((double)ld[ild][4]);

            /* Check if error E_infty should be computed. */
            if (ld[ild][2] != NO)
            {
              /* Compute the error E_infinity. */
              err_fd = X(error_l_infty_1_complex)(f, f_m, ld[ild][1], b,
                ld[ild][0]);
            }
          }

          /* Check if the fast NFSFT algorithm shall also be tested. */
          if (use_nfsft != NO)
          {
            /* Initialize cumulative time variable for the NFSFT algorithm. */
            t_f = 0.0;
          }
          else
          {
            /* Initialize cumulative time variable for the direct NDSFT
             * algorithm. */
            t_fd = 0.0;
          }

          /* Initialize time measurement. */
          t0 = getticks();

          /* Cycle through all runs. */
          for (i = 0; i < ld[ild][4]; i++)
          {
            /* Check if the fast NFSFT algorithm shall also be tested. */
            if (use_nfsft != NO)
            {
              /* Execute the adjoint NFSFT transformation. */
              nfsft_adjoint(&plan_adjoint);
            }
            else
            {
              /* Execute the adjoint direct NDSFT transformation. */
              nfsft_adjoint_direct(&plan_adjoint);
            }

            /* Multiplication with the Fourier-Legendre coefficients. */
            for (k = 0; k <= m[im]; k++)
              for (n = -k; n <= k; n++)
                f_hat[NFSFT_INDEX(k,n,&plan_adjoint)] *= a[k];

            /* Check if the fast NFSFT algorithm shall also be tested. */
            if (use_nfsft != NO)
            {
              /* Execute the NFSFT transformation. */
              nfsft_trafo(&plan);
            }
            else
            {
              /* Execute the NDSFT transformation. */
              nfsft_trafo_direct(&plan);
            }
          }

          /* Check if the fast NFSFT algorithm has been used. */
          t1 = getticks();

          if (use_nfsft != NO)
            t_f = nfft_elapsed_seconds(t1,t0);
          else
            t_fd = nfft_elapsed_seconds(t1,t0);

          /* Check if the fast NFSFT algorithm has been used. */
          if (use_nfsft != NO)
          {
            /* Calculate average time needed. */
            t_f = t_f/((double)ld[ild][4]);
          }
          else
          {
            /* Calculate average time needed. */
            t_fd = t_fd/((double)ld[ild][4]);
          }

          /* Check if error E_infty should be computed. */
          if (ld[ild][2] != NO)
          {
            /* Check if the fast NFSFT algorithm has been used. */
            if (use_nfsft != NO)
            {
              /* Compute the error E_infinity. */
              err_f = X(error_l_infty_1_complex)(f, f_m, ld[ild][1], b,
                ld[ild][0]);
            }
            else
            {
              /* Compute the error E_infinity. */
              err_fd = X(error_l_infty_1_complex)(f, f_m, ld[ild][1], b,
                ld[ild][0]);
            }
          }

          /* Print out the error measurements. */
          fprintf(stdout,"%e\n%e\n%e\n%e\n%e\n%e\n\n",t_d,t_dp,t_fd,t_f,err_fd,
            err_f);

          /* Finalize the NFSFT plans */
          nfsft_finalize(&plan_adjoint);
          nfsft_finalize(&plan);
        } /* for (im = 0; im < im_max; im++) - Process all cut-off
           * bandwidths.*/
      } /* for (ild = 0; ild < ild_max; ild++) - Process all node sets. */
    } /* for (ip = 0; ip < ip_max; ip++) - Process all parameter sets. */

    /* Delete precomputed data. */
    nfsft_forget();

    /* Check if memory for precomputed data of the matrix K has been
     * allocated. */
    if (precompute == YES)
    {
      /* Free memory for precomputed matrix K. */
      nfft_free(prec);
    }
    /* Free data arrays. */
    nfft_free(f);
    nfft_free(f_m);
    nfft_free(xi);
    nfft_free(eta);
    nfft_free(a);
    nfft_free(f_hat);
    nfft_free(b);

    /* Free memory for node sets. */
    for (ild = 0; ild < ild_max; ild++)
      nfft_free(ld[ild]);
    nfft_free(ld);

    /* Free memory for cut-off bandwidths. */
    nfft_free(m);

    /* Free memory for parameter sets. */
    for (ip = 0; ip < ip_max; ip++)
      nfft_free(p[ip]);
    nfft_free(p);
  } /* for (tc = 0; tc < tc_max; tc++) - Process each testcase. */

  /* Return exit code for successful run. */
  return EXIT_SUCCESS;
}